Algorithm 3 Movement Path Generation Algorithm

Input: $D=\left\{d_1,{ d}_2, \dots ,{ d}_n\right\}$ /* set of data to be clustered */

$L=\left\{l\left(d_i\right)\left|d=1, \dots , n\right.\right\}$ /* set of cluster labels of D */

$P=\left\{p_{11}, \dots ,{ p}_{\mathit{KK}}\right\}$ /* set of cluster transition matrix */

${\mathit{path}}_{\mathit{max}}$ /* maximum path length */

$m$ /* number of data to generate */

$K$ /* number of clusters */

$d_{\max }$ /* distance limit */

Output:$T=\left\{t_1, \dots ,{ t}_m\right\}$ /* set of sequential location data */

for $\mathit{iter}\leftarrow 1$ to $m$ do

$i\leftarrow k\in \left\{1, 2,\dots , K\right\}$;

$t_{\mathit{iter}}\leftarrow d_i\in D$ for all $l\left(d_i\right)=i$;

for $\mathit{path}\leftarrow 2$ to ${\mathit{path}}_{\mathit{max}}$ do

$i\leftarrow$$k\in \{1, 2,\dots , K|{\mathsf{p}}_i\}$;

${\mathrm{t}}_{\mathit{iter}}\leftarrow \mathrm{concat}(t_{\mathit{iter}},{ d}_i\in D$$\mathrm{for} \mathrm{all} l\left({ d}_i\right)=i)$;

end

end